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ASTRONOMY 181
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The SPECIAL Theory
of RELATIVITY
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Postulate 1
All physical laws must be equivalent
when described in INERTIAL reference
frames.
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Postulate 2
The speed of light must be measured to be
the same by all observers in inertial reference
frames.
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Consider two planets that are very distant from each other...
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They may communicate using pulses of light
….say, 3 min apart
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A rocket ship traveling between the planets would
see the flashes…but how far apart?
From the point of view of the rocket crew, it
could be that the flashes appear 6 min apart
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Let’s assume that the rocket has its own beacon
that flashes when they see a flash…
From the point of view of the rocket, they must flash every 6 min
From the point of view of the observer , the flashes are
simultaneous…3 min apart!!!
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The reverse situation: signals are sent from right
to left…
From the point of view of the rocket, they must flash every 1.5 min
From the point of view of the observer , the flashes are
simultaneous…3 min apart!!!
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Recall the Doppler shift…
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If the rocket flashes every 6 min:
AS IT APPROACHES US WE WOULD SEE
A FLASH EVERY 3 MIN
AS IT RECEEDS US WE WOULD SEE A
FLASH EVERY 12 MIN
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If the rocket travels from one planet to the other
and back again emitting a total of twenty flashes,
10 out and 10 back at a rate of 1 every 6 min, the
flashes can be used to time the trip.
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From the point of view of the rocket, flashes are
emitted every 6 min for the whole trip…
Outbound: 10 flashes @ 6 min/flash = 60 min
Inbound:
10 flashes @ 6 min/flash = 60 min
Total = 120 min = 2 hours
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From the point of view of the planet, flashes are
emitted every 12 min on the way out and every
3 min for the trip back…
Outbound: 10 flashes @ 12 min/flash = 120 min
Inbound:
10 flashes @ 3 min/flash = 30 min
Total = 150 min = 2.5 hours
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2 hours have passed
on the rocket
2.5 hours have passed on
the planet
TIME DILATION!!!
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EXAMPLE: A trip to Pluto
Pluto is 5 light hours away.
0.8c
0.999999c
Earth
System
6.25 hr
5.000005 hr
Rocket
System
3.75 hr
25 minutes
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In this course, we have learned:
•How the length of the earth year is known.
•How the shape and size of the earth is known.
•How the motion of the earth is known.
•How the mass of the earth is known.
•How the length of the periods of the planets are known.
•How the mass of the planets are known.
•How the chemical composition of celestial objects is known.
•Where many of the elements come from.
•How the evolution of stars is known.
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TWO IMPORTANT QUESTIONS REMAIN…
How do we know the SIZE
of our UNIVERSE?
How do we know the AGE
of our UNIVERSE?
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Remember that, looking out into
space is looking backward into
time.
OUR ESTIMATION OF THE
AGE OF THE UNIVERSE
DEPENDS ENTIERLY ON
OUT ESTIMATION OF HOW
LONG IT WOULD TAKE THE
UNIVERSE TO GET THIS BIG
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So, how big is the universe….
A QUICK REVIEW:
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Radar Ranging:
We measure distances in our solar
system by bouncing radio waves off
planets, for example.
Geometry helps us to interpret the
results.
Within one light-hour.
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Parallax:
The distances to objects
are determined by
observing apparent shifts
with respect to
background objects.
100 light-years
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Main-Sequence Fitting:
We know the distance to the Hades Cluster in
our own galaxy.
Comparing the luminosity of main sequence stars
in Hades to the main-sequence stars of other
clusters in our galaxy allows us to infer their
distances.
100,000 light-years
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Cepheid Variables:
There is a period-luminosity relation
for Cepheids.
Studying this relationship for
Cepheids nearby allows us to
determine the luminosity of
Cepheids in other, nearby galaxies.
10,000,000 light-years
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Distance Standards:
Luminosities of white dwarfs in nearby
galaxies are determined.
There is a rotational period-luminosity
relation for galaxies allowing us to
determine the luminosities of more distant
galaxies. (Tully-Fisher Relation)
10,000,000,000 light-years
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Abell 1835 IR 1916: Virgo Cluster: Red shift Factor 11
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IMPORTANT
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Time Dilation
Distance Luminosity Relation
Distance Standards
Stellar Parallax
Cepheid Variables
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NEXT TIME:
The END
OF THIS
COURSE
AS WE
KNOW IT…
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